Tensions in cosmology and prospects for cosmological constraints from reverberation mapping of active galactic nuclei

Current cosmology is at the cross-roads: enormous sucess of standard LambdaCDM model is undermined by the rumors of tensions. The most basic tension is the problem of the disagreement of the Hubble constant measured from the cosmic microwave background and from the local measurements of the expnasion rate, but a few more tensions are under consideration. I will review the issue, and I will report our recent cosmological results based on reverberation measurement of active galactic nuclei (AGN). I will also review the problems and prospects of Hubble constant measurement from this technique.